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Absolute value

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Source: — Problem Solving |

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by Brent@GMATPrepNow » Wed Jan 02, 2019 6:25 pm
harsh8686 wrote:If $$\left|X^2\ -\ 6\right|\ =\ X$$ , which of the following could be the value of x?

A) -2
B) 0
C) 1
D) 3
E) 5
A quick approach is to simply test the answer choices

A) -2 No good. The absolute value of something cannot be negative
B) 0 Plug in to get |0² - 6| = 0. Doesn't work.
C) 1 Plug in to get |1² - 6| = 1. Doesn't work.
D) 3 Plug in to get |3² - 6| = 3. WORKS!!!

Answer: D

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by GMATGuruNY » Wed Jan 02, 2019 10:28 pm
harsh8686 wrote:If $$\left|X^2\ -\ 6\right|\ =\ X$$ , which of the following could be the value of x?

A) -2
B) 0
C) 1
D) 3
E) 5
Alternate approach:

Since an absolute value cannot be negative -- implying that the right side of the equation must be NONNEGATIVE -- we know that x≥0.
If x²-6=x, we get:
x²-x-6=0
(x-3)(x+2) = 0
Only the factor in green implies a nonnegative option for x:
x-3=0
x=3.

The correct answer is D.
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answer

by jaetpu » Thu Jan 03, 2019 10:28 pm
harsh8686 wrote:If $$\left|X^2\ -\ 6\right|\ =\ X$$ , which of the following could be the value of x?

A) -2
B) 0
C) 1
D) 3
E) 5
Absolute values can be time-consuming to deal with, because you have to split into two different cases and work them out. In this situation, the approach Brent mentioned, testing the answer choices, will be the fastest approach.
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by Scott@TargetTestPrep » Fri Feb 01, 2019 5:43 pm
harsh8686 wrote:If $$\left|X^2\ -\ 6\right|\ =\ X$$ , which of the following could be the value of x?

A) -2
B) 0
C) 1
D) 3
E) 5
Looking at the answer choices we see that when x = 3, we have:

|9 - 6| = 3

3 = 3

Answer: D

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